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CBSE Questions for Class 11 Commerce Applied Mathematics Limits And Continuity     Quiz 5 - MCQExams.com

The limit of xsin(e1x) as x0
  • is equal to 0
  • is equal to 1
  • is equal to e2
  • does not exist
The function represented by  the following graph is.

572668_db4e79fb2abd478fa7332735dca6ad0f.png
  • Differentiable but not continuous x=1
  • Neither continuous nor Differentiable at x=1
  • Continuous but not Differentiable at x=1
  • Continuous but Differentiable at x=1
If [x] denotes the greatest integer not exceeding x and if the function f defined by f(x)={a+2cosxx2(x<0)btanπ[x+4](x0) is continuous at x=0, then the order pair (a, b) =
  • (2,1)
  • (2,1)
  • (1,3)
  • (2,3)
limx01cosxx2 is ____
  • 2
  • 3
  • 12
  • 13
If limxx3+1x2+1(ax+b)=2, then
  • a=2 and b=1
  • a=1 and b=1
  • a=1 and b=1
  • a=1 and b=2
limx0(27+x)1/339(27+x)2/3  equals :
  • 1/6
  • 1/6
  • 1/3
  • 1/3
The value of the constant α and β such that limx(x2+1x+1αxβ)=0 are respectively.
  • (1,1)
  • (1,1)
  • (1,1)
  • (0,1)
What is limx0x2sin(1x) equal to ? 
  • 0
  • 1
  • 1/2
  • Limit does not exist.
If the function f(x) satisfies limx1f(x)2x21=π, then limx1f(x)=
  • 2
  • 3
  • 1
  • 0
The limit of [1x2+(2013)xex11ex1] as x0
  • Approaches +
  • Approaches
  • Is equal to loge(2013)
  • Does not exist
limx0loge(1+x)3x1= ____.
  • loge3
  • 0
  • log3e
  • 1
The limit of 1000n=1(1)nxn as x
  • does not exist
  • exists and equals to 0
  • exists and approaches +
  • exists and approaches
Which one of the following statements is correct?
  • limx0(fog)(x) exists.
  • limx0(gof)(x) exists.
  • limx0(fog)(x)=limx0(gof)(x)
  • limx0+(fog)(x)=limx0(gof)(x)
The limit of {1x1x1+1x2} as x0
  • Does not exist
  • Is equal to 12
  • Is equal to 0
  • Is equal to 1
limxπ6sin(xπ6)32cosx is equal to :
  • 0
  • 1(32)
  • 1
Evaluate: limx10x2100x10
  • 10
  • 5
  •  20
  • 5
limx0(25)x2(15)x+9xcos6xcos2x is equal to :
  • log(53)
  • 14log15
  • 116(53)2
  • log(35)
limxπ/4tanx1cos2x is equal to
  • 1
  • 0
  • 2
  • 1
If limx0xasinbxsin(xc),a,b,c,R{0} exists and has non-zero value, then 
  • a,b,c are in A.P
  • a,b,c are in G.P
  • a,b,c are in H.P
  • none of these
limx3=x3x29 is equal to
  • 1
  • 3
  • 3
  • 3
  • 0
The value of limxπ/62sin2x+sinx12sin2x3sinx1 is
  • 3
  • 3
  • 6
  • 0
If f(x)=|sinxcosxtanxx3x2x2x11|, then limx0f(x)x2 is
  • 1
  • 3
  • 1
  • Zero
If limnn.3nn(x2)n+n.3n+13n=13, then the range of x is (When nN)
  • [2, 5)
  • (1, 5)
  • (1, 5)
  • (, )
limx3(x34)/(x+1)=
  • (4/23)
  • (2/23)
  • (1/8)
  • (23/4)
limxπ2(π2xcosx) is equal to :
  • π+2
  • π2
  • e
  • e1
Determine the value of k for which the following function is continuous at x=3.
f(x)=x29x3,x3

f(x)=k,x=3
  • 2
  • 4
  • 6
  • 8
If f(x)=|cosxx12sinxx22x tanxx1|, then limx0f(x)x.
  • Exists and is equal to 2
  • Does not exist
  • Exist and is equal to 0
  • Exists and is equal to 2
Which of the following statements are true for the function f(x) defined for 1x3 in the figure shown?

880039_ce1751dc863440c2a77ba31deb50b922.png
  • limx1+f(x)=1
  • limx2f(x) does not exist
  • limx1f(x)=2
  • limx0+f(x)=limx0f(x)
limh0(h+1)2limh0(1+h)2/h is equal to
  • e1
  • e2
  • e2
  • e1
limx0(1cos2x)(3+cosx)xtan4x is equal to

  • 2
  • 1/2
  • 4
  • 3
Evaluate the limit:
limx0(xsinxx)sin(1x)
  • 1
  • 1
  • Does not exist
  • 0
limx0+((xcosx)x+(cosx)1lnx+(xsinx)x) is equal to
  • 2
  • 2+e
  • 2+1e
  • 3
If the function f(x)=ex2cosxx2 for x0 continuous at x=0 then f(0)=
  • 12
  • 32
  • 2
  • 13

The function f:R/0R given by f(x)=1x2e2x1 can be made continuous at x=0 by
defining f(0) as 

  • 0
  • 1
  • 2
  • -1
limx0esinx1x=
  • 0
  • 1
  • 1
  • none of these
Let Pn=nk=2(11k+1C2). If limxPn can be expressed as lowest rational in the form ab , then value of (a+b) is __________.
  • 12
  • 4
  • 8
  • 10
If limx0(cosx+asinbx)1x=e2 then
the possible values of a&bare: 
  • a=1,b=2
  • a=2,b=1
  • a=3,b=2/3
  • a=2/3,b=3
limxπ2tanx=
  • 0
  • does not exist
Suppose the function f(x)f(2x) has the derivative 5 at x=1 and derivative 7 at x=2. The derivative of the function f(x)f(4x) at x=1, has the value equal to?
  • 19
  • 9
  • 17
  • 14
limx0log(tan2x)(tan22x)=
  • 1
  • 2
  • 12
  • Does not exist
The value of limx01cos2xx equals
  • 0
  • 1
  • 2
  • Does not exist
If l=limx0x(1+a cosx)b sinxx3 is finite, 
 where lR, then 
  • (a)(a,b)=(1,0)
  • (b) a & b are any real numbers
  • (c)l=0
  • (d)l=12
limh0x+hxh is equal to 
  • x
  • 12x
  • 2x
  • 1x
Evaluate:
limx0(1+ax)1x
  • ea
  • e1a
  • 1
  • None of these
The value of limx01cosxx2
  • 12
  • 14
  • 2
  • none of these
lim x0cosx2cosx22cosx23......cosx2n is equal to 
  • 1
  • 1
  • sinxx
  • xsinx
limx01cosxx2=
  • 4
  • 2
  • 12
  • 1
limx11cos2(x1)x1
  • Exists and it equals 2
  • Exists and it equals 2
  • Does not exist because x10
  • Does not exist because left hand limit is not equal to right hand limit
limx0sin[cosx]1+[cosx] is
  • 1
  • 0
  • does not exist
  • 2
limx0e4x1x
  • 1
  • 3
  • 4
  • 2
0:0:1


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